Question

Simplify the following :-

1) 12 power 6 divide (3 power 4 x 4 power 3)
2) 18 power 8 divide 6 power 9 x 2 power 3
3) x/4 +x/5
4) 12x'2 /15y'2 divide 18xz'2/25y'2z

Answer 1

$\huge{\bf{\underline{\purple{Solution :}}}}$

Question - 1)

$\large{\star} \huge{\bold{12^{6} \div (3^{4} \times 4^{3} )}}$

$\implies \bold{\frac{12^{6} }{3^{4} \times 4^{3} }}$

$\implies \bold{\frac{3^6 \times 4^6}{3^4 \times 4^3}}$

$\implies \bold{3^{6-4} \times 4^{6-3}}$

$\implies \bold{3^2 \times 4^3}$

$\implies \bold{9 \times 64}$

$\implies \boxed{\bold{576}}$

Question -2)

$\huge{\star} \bold{18^{8} \div 6^{9} \times 2^3}$

$\implies \bold{\frac{18^8}{6^9} \times 2^3}$

$\implies \bold{\frac{(6 \times 3)^{2} }{6^{9}}\times 2^3}}$

$\implies \bold{\frac{6^8 \times 3^8}{6^9}} \times 2^3$

$\implies \bold{\frac{3^8 \times 2^3}{6}}$

$\implies \bold{\frac{3^{7+1} \times 2^{2+1}}{6}}$

$\implies \bold{\frac{3^7 \times 3 \times 2^2 \times 2}{6}}$

$\implies \bold{3^7 \times 2^2}$

$\implies \bold{2187 \times 4}}$

$\implies \boxed{\bold{8748}}$

Question -3)

$\huge{\star} \bold{\frac{x}{4} + \frac{x}{5}}$

$\implies \bold{\frac{5x + 4x}{20}}$

$\implies \boxed{\bold{\frac{9x}{20}}}$

Question - 4)

$\huge{\star} \bold{\frac{12x^2}{15y^2} \div \frac{18xz^2}{25y^2z}}$

$\implies \bold{\frac{12x^2}{15y^2} \times \frac{25y^2z}{18xz^2}}$

$\boxed{\bold{\frac{10x}{9z}}}$

$\rule{200}2$

Answer 2

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Problems:-}}}}}}$

1) 12 power 6 divide (3 power 4 x 4 power 3)

2) 18 power 8 divide 6 power 9 x 2 power 3

3) x/4 +x/5

4) 12x'2 /15y'2 divide 18xz'2/25y'2z

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answers:-}}}}}}$

See the attachments above✌